Correlation Functions of Heavy Operators in AdS/CFT

Abstract

In this thesis we investigate the holographic dual description of correlation functions of heavy operators in conformal field theory. These heavy operators have scaling dimension that scales with the CFT central charge in the large central charge limit, and they are dual to objects propagating through the bulk whose gravitational backreaction cannot be neglected. We reproduce the expected CFT correlation functions through a gravitational path integral calculation–one that requires the introduction of special terms associated to the horizons of black holes appearing in the gravitational configurations. The results for two point functions apply in arbitrary dimensions. We also discuss heavy-heavy-light-light correlation functions in various dimensions. We find results for the three point functions in two-dimensional CFT that are consistent with the expected universal behavior of heavy operator structure constants. This is consistent with the interpretation of three-dimensional Einstein gravity as the holographic dual to an ensemble of CFT2’s.